Title:
The quantum state can be interpreted statistically

Abstract: Many quantum physicists have suggested that a quantum state does not
represent reality directly, but rather the information available to some agent
or experimenter. This view is attractive because if a quantum state represents
only information, then the collapse of the quantum state on measurement is
possibly no more mysterious than the Bayesian procedure of updating a
probability distribution on the acquisition of new data. In order to explore
the idea in a rigorous setting, we consider models for quantum systems with
probabilities for measurement outcomes determined by some underlying physical
state of the system, where the underlying state is not necessarily described by
quantum theory. A quantum state corresponds to a probability distribution over
the underlying physical states, in such a way that the Born rule is recovered.
We show that models can be constructed such that more than one quantum state is
consistent with a single underlying physical state-in other words the
probability distributions corresponding to distinct quantum states overlap. A
recent no-go theorem states that such models are impossible. The results of
this paper do not contradict that theorem, since the models violate one of its
assumptions: they do not have the property that product quantum states are
associated with independent underlying physical states.